Daly, A., and Bierlaire, M. (2003)

A general and operational representation of GEV models

Generalised Extreme Value models provide an interesting theoret- ical framework to develop closed-form random utility models. Unfor- tunately, few instances of this family are to be found as operational models in practice. The form of the model, based on a generating function G which must satisfy specific properties, is rather compli- cated. Fundamentally, it is not an easy task to translate an intuitive perception of the correlation structure by the modeller into a concrete G function. And even if the modeller succeeds in proposing a new G function, the task of proving that it indeed satises the properties is cumbersome. The main objectives of this paper are (i) to provide a general theo- retical foundation, so that the development of new GEV models will be easier in the future, and (ii) to propose an easy way of generating new GEV models without a need for complicated proofs. Our technique requires only a network structure capturing the underlying correlation of the choice situation under consideration. If the network complies with some simple conditions, we show how to build an associated model. We prove that it is indeed a GEV model and, therefore, complies with random utility theory. The Multinomial Logit, the Nested Logit and the Cross-Nested Logit models are specific instances of our class of models. So are the recent GenL model, combining choice set generation and choice model and some specialised compound mod- els used in recent work. Probability, expected maximum utility and elasticity formulae for the class of models are provided.

- Daly and Bierlaire, 2006
- Daly, A., and Bierlaire, M. (2006). A General and Operational Representation of Generalised Extreme Value Models,
*Transportation Research Part B: Methodological***40**(4):285-305. - ISI 2004: Impact factor: 2.856, cited half-life: 9.1